value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Percent of a number, Pay $40 for plan offered for $30 for plan what percent...

Pay $40 for plan offered for $30 for plan what percentage of savings

speed of the truck , A man travels 600km partly by train and partly by tru...

A man travels 600km partly by train and partly by truck. If he  covers 120km by train and the rest by truck, it takes him eight hours. But, if he travels 200km by train and the res

Caselets, how are indian customers visiting shoppers stop any different fro...

how are indian customers visiting shoppers stop any different from customers of developed western countries

Arc length - applications of integrals, Arc Length - Applications of integr...

Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function.  As it's sufficiently easy to derive the formulas that we'

Infinite, why cant we find the value of 1 upon zero

why cant we find the value of 1 upon zero

General math, Kwai made 5 pints of iced tea. How many cups of tea did he ma...

Kwai made 5 pints of iced tea. How many cups of tea did he make?

Determine the length of the longer base, The longer base of a trapezoid is ...

The longer base of a trapezoid is 3 times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trape

What is the new cost of the pants, A pair of pants costs $24. The cost was ...

A pair of pants costs $24. The cost was decreased by 8%. What is the new cost of the pants? If the cost of the pants is decreased by 8%, the cost of the pants is 92 percent of

The sum of two consecutive integers is 41 integer, The sum of two consecuti...

The sum of two consecutive integers is 41. What are the integers? Two consecutive integers are numbers in sequence like 4 and 5 or -30 and -29, that are each 1 number apart. Le

Minimax regret method -decision making under uncertainty, MINIMAX regret me...

MINIMAX regret method Minimax method assumes that the decision maker will experience 'regret' after he has made the decision and the events have happened. The decision maker ch

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd